London has been battered by 50mph winds that have felled trees and caused travel chaos. Powerful gusts swept across the capital as the Met Office issued a yellow "be aware" weather alert for most of the country.

The Trocadero is to be turned into a "pod" hotel offering tiny rooms at knock-down prices.

With rooms of just 12 square metres and 17 square metres, the hotel aims to be London's answer to the Pod Hotel in New York and will occupy part of the second to seventh floors in the Grade II-listed building in Piccadilly Circus.

Corridors will run around the outside of the building, and 495 rooms, all ensuite, will be grouped around internal courtyards. A planning application for the scheme, provisionally named the Piccadilly Hotel, will come before Westminster council this week.

New York's Pod Hotel has a loyal following among travellers and critics. The Washington Post praised its design that made the best use of the bedrooms' 10ft by 10ft floorspace.

The newspaper's travel writer Gary Lee wrote: "The Pod is proof that you can be hip on a budget. The rooms are all equipped with iPod docking stations, LCD televisions and free wi-fi. The decor is an inviting mix of mod and Fifties retro." On the downside: "Almost half the rooms have shared baths, and the walls are thin enough that you hear doors shutting down the hall."

National Geographic Traveler magazine described it as: "Hostelling for the 21st century, updated for global flashpackers." The hotel has been reviewed more than 1,100 times on travel website Tripadvisor - and scored an approval rating of 88 per cent, making it one of the most popular in the city.

Some reviewers found the rooms claustrophobic, but others felt the low prices justified the squeeze. Emma Mills, from London, stayed at the hotel in May. She said: "It was compact, but when you're in New York you're not there to sit in a room. I would much rather stay there and have more shopping money."

The Trocadero plan would be a boost for property investor Asif Aziz, whose Golfrate Holdings purchased the building for £225million in 2005. Since then the centre is said to have struggled to attract tenants and, in January, lost one of its most high profile, Planet Hollywood, after 16 years. The restaurant has moved to a new £5million venue in Haymarket. The floors above the third level have been vacant since indoor theme park Segaworld moved out. Westminster's report raises concerns over the lack of natural light or ventilation in rooms. But adds: "It will provide affordable accommodation for visitors to this part of London."

ReviewTom Teodorczuk, in New York

It's goodbye Planet Hollywood, hello Planet Parsimony. I checked into the original New York pod establishment to see what is coming to the West End.

Tom Teodorczuk in New York’s Pod Hotel

In less than two years, the Pod Hotel in Midtown Manhattan has carved a niche offering a boutique experience at a no-frills price.

Everything is scaled down. The lift is narrower than a matchstick and the Broadway show flyers are smaller than playing cards. Once I got over how minuscule my £72-a-night minimalist room with ensuite shower was, I relaxed.

The flat-screen TV and wi-fi worked fine and the iPod dock meant I could shuffle my own music. But the frosty white wall was littered with black smudges and the bed was not as soft or comfy as I'd have liked. But the Pod supplied a tranquil experience away from the urban noise, impressive in a city that thrives on not sleeping. When it comes to the Trocadero, it will be ideal for cost-conscious culture vultures or business execs needing to brood prior to a Piccadilly meeting.